Based on the provided data concerning the tournament performance of six different players, answer the following questions: | Player | Matches Played | Run Average | Balls Faced | Strike Rate | |---|---|---|---|---| | A | 8 | — | — | 129.6 | | B | 20 | 81 | — | — | | C | — | 38 | 400 | 114 | | D | — | — | — | 72 | | E | 28 | 55 | 1280 | — | | F | — | — | — | 66 | Important Guidelines: 1. Strike Rate is calculated as (Total Runs / Balls Faced) * 100. 2. Every player batted in every match they played. 3. Hyphens (-) indicate missing data points that must be derived to solve the problems. Determine the total number of matches that player C participated in during the tournament.

### Concept & Inverse Calculation To find the number of matches, you must first calculate the total runs using the strike rate and balls faced, then divide by the run average. $$ \text{Total Runs} = \left( \frac{\text{Strike Rate}}{100} \right) \times \text{Balls Faced} $$ $$ \text{Matches} = \frac{\text{Total Runs}}{\text{Run Average}} $$ ### Step-by-Step Solution 1. **Extract Data for C:** - Strike Rate = 114 - Balls Faced = 400 - Run Average = 38 2. **Calculate Total Runs:** - Total Runs = $\left( \frac{114}{100} \right) \times 400 = 114 \times 4 = 456$ 3. **Calculate Matches Played:** - Matches = $\frac{456}{38}$ - Simplify: $\frac{456}{38} = 12$ ### Exam Strategy & Shortcut Notice the multiples: $38 \times 10 = 380$. $456$ is $76$ more than $380$, which is exactly $38 \times 2$. Hence, $10 + 2 = 12$ matches. ### Common Pitfall Misapplying the strike rate formula (e.g., dividing by strike rate instead of multiplying) will result in an incorrect total runs calculation, derailing the final step. ### Final Answer Therefore, the correct answer is **12**.